Due to uncertainty in demand, sometimes management may delay their planning of shifts later in the horizon when they have more information. We consider a novel dynamic and flexible system for scheduling personnel for work shifts planned at the last minute called 'on-call' shifts. The flexibility in the system allows employees to freely select or reject shifts offered to them. Senior employees may also replace or bump junior employees from the current schedule if no other shift of their choice is available provided certain conditions are met. The operator seeks to quickly assign all available shifts to employees while ensuring minimum total bumps. We develop several easy-to-implement policy approximations as well as deep reinforcement learning-based policies to efficiently operate the system. A comparison of all the developed policies is made using real data from our industrial partner. We identify the best policies under different settings and significantly improve upon the current practices.
